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I find time dilation confusing so I'm not sure if it is a relevant factor.

Lets say you have a spaceship. There's no such thing as faster than light travel, but you do have inertial dampener technology that allows you to accelerate at very high G's without obliterating yourself.

You want to get to a nearby star system as soon as possible. When I say "soon" I mean early on the timeline of the destination star system, not necessarily as quick as possible according to your own perspective of the voyage duration. In other words, you want to intervene in the events of the destination before they progress to far into the future.

Is there a maximum rate of acceleration or top speed you could reach before time dilatation causes you to actually arrive later than you would have at a lower speed?

What about if you want to go there and then get back before your friends at home get any older?

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  • $\begingroup$ You might be better off asking this in the Physics Stack Exchange $\endgroup$ – nzaman Sep 2 '17 at 12:52
  • $\begingroup$ @nzaman I doubt that the physics stack exchange would be supportive. If they answered it, they would simply state that time dilation happens at ANY speed, but the faster you go, the greater the dilation. Time goes slower the faster you go. $\endgroup$ – Justin Thyme Sep 2 '17 at 14:02
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You cannot get there faster than light (from the perspective of the places you are traveling from and to, if they are [nearly] at rest with respect to each other (meaning even if they are both moving, the distance between them is not increasing or decreasing by more than a few miles per second).

If they are 10 LY apart, it takes ten years of their time for a signal (or anything within a few percent of the speed of light) to move between them.

This also means you cannot know what is happening on B if you are sitting on A, and vice versa. No kind of signal known to physics, not even a gravity wave, travels faster than light. If a revolution occurs on B, the people on A won't hear about it for ten years. Then it would take them at least ten years to get there and respond.

Now, traveling at near light speed (say 99.99% and they have an unlimited energy supply to do it) the amount of time that passes for the passengers is contracted by a factor 70.71. So 10 years, or 3650 days, the passengers, ship and everything in it will only age 51.6 days. (This is not a "feels like" but actual time passage.)

Also note that when they arrive at B, it will have been 20 years since the message about the revolution was first sent. (They may know more about what happened in that 20 years by capturing signals from B along the way there, so they may be up to speed when they land.)

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No. Time dilatation affects how you (the traveller) sense the duration of the voyage. It does not change the simple fact that if the star systems are 9 light year apart and you are travelling with 0.9 c relative to them it will take 10 years (according to the observer resting in one of the star systems) to get there. So if you travel at higher speed, you will always arrive earlier.

However, since your apparent mass increases with relativistic speeds, if your energy budget on the ship is limited, it might be pointless to accelerate further after reaching 0.95 c. It will shorten your voyage (according to the observer resting in one of the star systems) only a little bit, regardless how much energy you use up.

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    $\begingroup$ "The difference between 9 years and a day to go ten light years and 9 years and a week to go ten light years is an awful lot of energy, so why not just take it steady and enjoy the extra 6 days staring at the void?" +1 $\endgroup$ – Joe Bloggs Sep 2 '17 at 13:36
  • $\begingroup$ @Joe Bloggs for the same reason yahoos on earth will overtake you, just to wait at the next stoplight. $\endgroup$ – Justin Thyme Sep 2 '17 at 14:06
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You don't understand time dilation.

Let me explain in the simplest possible way.

  • to anyone not accelerating (too much) and moving at a speed slow compared with speed of light time will appear to flow at a constant rate and synchronously with any other "slow" observer.
  • the above means both starting point and destination are on the same clock time. You cannot change their wall clock (unless you accelerate the whole planet to near light-speed)
  • when something (your spaceship) accelerates to a sizable fraction of light-speed its wall-clock will seem to slow down as seen from the "static" observers (i.e.: from both start and arrival points).
  • people on board of the speeding vehicle will not have any feeling of this "slowdown" and they would see the Universe around evolve at a higher speed instead.
  • this gives a way to intuitively understand why it isn't possible to accelerate to reach the speed of light:
    • you accelerate at constant rate in your time
    • acceleration is variation of speed in the unit time
    • your time, seen from outside, is slower the faster you go.
    • your "unit time" gets longer, as seen from outside.
    • your acceleration diminishes, as seen from outside, when you go faster.
    • when you are very near to light-speed your time seems to freeze, so you are not accelerating anymore.
    • you cannot reach speed of light, even if you are (subjectively) still accelerating at the same rate.

Back to your question:

  • the fastest you go the sooner you'll arrive (unsurprisingly!) in all reference systems (start, arrival and local to spaceship.
  • You have no way to arrive before a photon starting together with you.
  • if you gain enough speed the crew of spaceship will arrive in a very short time (depends on actual speed), possibly much less than the light-speed equivalent of distance.
  • this time will be, however, the same, as seen from the "static" endpoints.
  • if you are going to a system 10 light-years travel can take no less than 10 years (actually it will be more, since you cannot travel at light speed).
  • if you go really fast crew may have seen only a few months passing, but the time passed on destination will be more than 10 years.
  • if you make a round trip crew (and everything on board) will have aged some more months, but at their arrival back on Earth more than 20 years would have passed.

Time dilation (clock slowdown) applies only to spaceship (accelerating object).

"Static" (non-accelerating) objects will continue to clock time normally.

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